I don't have kids yet, but I'm planning on homeschooling and I think using travel for education sounds like a fantastic idea. A lot of people on this forum are math/science focused, but traveling would be a great way to explore language, history, culture, and geography. AND it would actually be INTERESTING! Lots of kids find these subjects boring because they're learning it from a textbook. But being in a new place and seeing the battlefields, architectural ruins, talking to native speakers, using maps to plan your travels... not only is it more engaging, but your child is more likely to remember it!
When I started traveling (as an adult) I kept a travel diary. I'd draw a map of the country I was going to be in with important locations (mountains, rivers, capital, big cities etc., as well as the towns I would be traveling to). I often did this before I left home just to get to know the new country a little bit better. I'd also make a list of words and phrases in whatever language they spoke (I'd leave a bit of room here to add to it as I traveled and learned more). Once I left home, I'd spend some time each night taking notes on my day. Where I went, what I saw, what the people were like... But I also took notes on what I learned. When I'd visit a museum or take a tour, I'd learn all sorts of interesting facts. Writing them down helped to organize my thoughts as well as make it a little more likely I'll remember (and if I forget, I can always go back and look it up!). I found it so enjoyable and helpful, that I've continued to do this even when I'm just going on a trip within the USA. Finding a fun journal to take notes in is a normal part of my pre-trip planning process. I don't normally keep a diary, but I always do travel diaries!